Ultra-short-period exoplanets like K2-141 b likely have magma oceans on their dayside, which play a critical role in redistributing heat within the planet. This could lead to a warm nightside surface, measurable by the James Webb Space Telescope, offering insights into the planet's structure. Accurate models of properties like viscosity, which can vary by orders of magnitude, are essential for such studies. We present a new model for predicting molten magma viscosity, applicable in diverse scenarios, including magma oceans on lava planets. Using a database of 28,898 viscosity measurements on phospho-alumino-silicate melts, spanning superliquidus to undercooled temperatures and pressures up to 30 GPa, we trained a greybox artificial neural network, refined by a Gaussian process. This model achieves high predictive accuracy (RMSE $\approx 0.4 \log_{10}$ Pa$\cdot$s) and can handle compositions from SiO$_2$ to multicomponent magmatic and industrial glasses, accounting for pressure effects up to 30 GPa for compositions such as peridotite. Applying this model, we calculated the viscosity of K2-141 b's magma ocean under different compositions. Phase diagram calculations suggest that the dayside is fully molten, with extreme temperatures primarily controlling viscosity. A tenuous atmosphere (0.1 bar) might exist around a 40{\deg} radius from the substellar point. At higher longitudes, atmospheric pressure drops, and by 90{\deg}, magma viscosity rapidly increases as solidification occurs. The nightside surface is likely solid, but previously estimated surface temperatures above 400 K imply a partly molten mantle, feeding geothermal flux through vertical convection.

本研究针对超短周期系外行星如K2-141 b中存在的熔岩海洋，建立了一个新的铝硅酸盐熔体粘度预测模型，填补了熔体物理性质建模的空白。通过使用28898条粘度测量的数据，模型展示了高准确性，并能用于多种熔融物质的情况。研究结果表明，该模型可用于理解熔岩行星的表面特性及其温度分布，推动了对这类行星的深入研究。

铝硅酸盐熔体粘度的一般机器学习模型及其在干熔岩行星表面特性的应用